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Chapter 4: Problem 97

Oliver has a mass of \(76.2 \mathrm{kg} .\) He is riding in an elevator that has a downward acceleration of \(1.37 \mathrm{m} / \mathrm{s}^{2} .\) With what magnitude force does the elevator floor push upward on Oliver?

Short Answer

Expert verified
Answer: The magnitude of the force exerted by the elevator floor on Oliver is 642.888 N.

Step by step solution

01

1. Identify Knowns and Unknowns

We have the following information given: - Oliver's mass (m): \(76.2 \mathrm{kg}\) - The elevator's downward acceleration (a): \(1.37 \mathrm{m} / \mathrm{s}^{2}\) - Gravitational acceleration (g): \(9.81 \mathrm{m} / \mathrm{s}^{2}\) Our objective is to determine the force exerted by the elevator floor on Oliver.
02

2. Express Newton's Second Law of Motion

The force exerted by the elevator on Oliver, denoted as F, is given by Newton's second law of motion, which states that the force is equal to the mass multiplied by the acceleration. F = m × a However, we need to consider the effects of gravity on Oliver. The gravitational force acting on him can be calculated by: Gravitational Force = m × g Thus, the net force acting on Oliver inside the elevator is the difference between gravitational force and force exerted by the elevator floor.
03

3. Calculate the Gravitational Force

Calculate Oliver's gravitational force using the given mass and gravitational acceleration: Gravitational Force = m × g = 76.2 kg × 9.81 m/s² = 747.282 N (Keep the units to ensure consistency in the final calculation.)
04

4. Calculate the Net Force Acting on Oliver

Now, we'll calculate the net force acting on Oliver using his mass and the elevator's acceleration: Net Force = m × a = 76.2 kg × 1.37 m/s² = 104.394 N
05

5. Calculate the Force Exerted by the Elevator Floor

Since the net force acting on Oliver is the difference between the gravitational force and the force exerted by the elevator floor (F), we can solve for the force exerted by the elevator floor: F = Gravitational Force - Net Force = 747.282 N - 104.394 N = 642.888 N The elevator floor pushes upward on Oliver with a magnitude force of 642.888 N.

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Most popular questions from this chapter

A 50.0 -kg crate is suspended between the floor and the ceiling using two spring scales, one attached to the ceiling and one to the floor. If the lower scale reads \(120 \mathrm{N},\) what is the reading of the upper scale? Ignore the weight of the scales.
During a balloon ascension, wearing an oxygen mask, you measure the weight of a calibrated \(5.00-\mathrm{kg}\) mass and find that the value of the gravitational field strength at your location is 9.792 N/kg. How high above sea level, where the gravitational field strength was measured to be $9.803 \mathrm{N} / \mathrm{kg},$ are you located?
A sailboat, tied to a mooring with a line, weighs \(820 \mathrm{N}\) The mooring line pulls horizontally toward the west on the sailboat with a force of $110 \mathrm{N}$. The sails are stowed away and the wind blows from the west. The boat is moored on a still lake-no water currents push on it. Draw an FBD for the sailboat and indicate the magnitude of each force.
A bag of potatoes with weight \(39.2 \mathrm{N}\) is suspended from a string that exerts a force of \(46.8 \mathrm{N}\). If the bag's acceleration is upward at \(1.90 \mathrm{m} / \mathrm{s}^{2},\) what is the mass of the potatoes?
Find the altitudes above the Earth's surface where Earth's gravitational field strength would be (a) two thirds and (b) one third of its value at the surface. [Hint: First find the radius for each situation; then recall that the altitude is the distance from the surface to a point above the surface. Use proportional reasoning.]
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